The aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz

In this thesis, we introduced some types of fibrewise topological spaces by using a near soft set, various related results also some fibrewise near separation axiom concepts and a fibrewise soft ideal topological spaces. We introduced preliminary concepts of topological spaces, fibrewise topology, soft set theory and soft ideal theory. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise soft near topological spaces, Also, we show the notions of fibrewise soft near closed topological spaces, fibrewise soft near open topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces. On the other hand, we studied fibrewise soft near forms of the more essent

In this thesis, we introduced some kinds of fibrewise topological spaces by using totally continuous function is called fibrewise totally topological spaces. We generalize some fundamental results from fibrewise topology into fibrewise totally topological spaces. We also introduce the concepts of fibrewise totally separation axioms, fibrewise totally compact and locally totally compact topological spaces. As well as fibrewise totally perfect topological spaces. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise totally topological spaces. We, also introduce the concepts of fibrewise totally closed topological spaces, fibrewise totally open topological spaces, fibrewise locally sliceable and locally s

This paper is devoted to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuzzy -ω-topological spaces, weakly fibrewise fuzzy -ω-topological spaces and strongly fibrewise fuzzy -ω- topological spaces. Also, Several characterizations and properties of this class are also given as well. Finally, we focused on studying the relationship between weakly fibrewise fuzzy -ω-topological spaces and strongly fibrewise fuzzy -ω-topological spaces.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near topological spaces over B. Also, we introduce the concepts of fibrewise near closed and near open topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

In this work we define and study new concept of fibrewise topological spaces, namely fibrewise soft topological spaces, Also, we introduce the concepts of fibrewise closed soft topological spaces, fibrewise open soft topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces.

We define and study new ideas of fibrewise topological space on D namely fibrewise multi-topological space on D. We also submit the relevance of fibrewise closed and open topological space on D. Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space on D. Furthermore, we propose and prove a number of statements about these ideas.

Fibrewise topological spaces theory is a relatively new branch of mathematics, less than three decades old, arisen from algebraic topology. It is a highly useful tool and played a pivotal role in homotopy theory. Fibrewise topological spaces theory has a broad range of applications in many sorts of mathematical study such as Lie groups, differential geometry and dynamical systems theory. Moreover, one of the main objects, which is considered in fibrewise topological spaces theory is connectedness. In this regard, we of the present study introduce the concept of connected fibrewise topological spaces and study their main results.